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Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$
Learn how to solve definite integrals problems step by step online.
$\frac{d}{dx}\left(x^{\frac{1}{3}\ln\left(\sin\left(8x\right)\right)}\right)$
Learn how to solve definite integrals problems step by step online. Find the derivative using logarithmic differentiation method d/dx(x^ln(sin(8x)^1/3)). Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). To derive the function x^{\frac{1}{3}\ln\left(\sin\left(8x\right)\right)}, use the method of logarithmic differentiation. First, assign the function to y, then take the natural logarithm of both sides of the equation. Apply natural logarithm to both sides of the equality. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x).